`sin3x+sin2x-sinx=4sinxcos(x/2)cos(3x/2)`

Prove that: (i) sin 3x+"sin" 2x-"sin" x = 4 sin x cos((x)/(2))cos((3x)/(2)) (ii) ("sin" 3x+"sin" x)"sin" x+(cos 3x-cos x)cos x=0.

Prove the following Identities sin x +sin 2x + sin 4x +sin 5x = 4 cos(x/2).cos((3x)/2)sin3x

The value of the limit lim_(x rarr(pi)/(2))((4sqrt(2)(sin3x+sin x))/((2sin2x sin(3x/2)+cos(5x/2))-(sqrt(2)+sqrt(2)cos2x+cos(3x/2))))=

Find the gereral of the equation sinx-3sin2x+sin3x=cosx-3cos2x+cos3x .

The number of solutions of the equation sinx-sin2x+sin3x=2cos^(2)x-cosx" in "(0,pi) is

sin_( if )x+sin2x+sin3x=cos x+cos2x+cos3x

int(3sinxcos^(2)x-sin^(3)x)dx

The number of values of x between 0 and 2 pi that satisfies the equation sin x+sin2x+sin3x=cos x+cos2x+cos3x must be